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3 years ago

Solve x^2 – 3x = 18 by factoring.

Mathematics

1 answer:

Ganezh [65]3 years ago

6 0

Answer:

Step-by-step explanation:

x²-6x+3x-18=0

x(x-6)+3(x-6)=0

(x+3)(x-6)=0

x=-3 or 6

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Find the slope of the line that passes through (1,6) and (4,4)

Vadim26 [7]

Answer:

y=-2/3x+20/3

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(4-6)/(4-1)

m=-2/3

y-y1=m(x-x1)

y-6=-2/3(x-1)

y=-2/3x+2/3+6

y=-2/3x+2/3+18/3

y=-2/3x+20/3

8 0

3 years ago

Factor the expression using the GCF.<br> 60 – 36 =

Ivanshal [37]

Answer

12 (5 - 3)

Step-by-step explanation:

The greatest common factor is the largest number that will divide both numbers evenly. As an example, 6 is a common factor because it divides both 60 and 36. However, it is not the greatest common factor.

If I break 60 into it's prime factors, I would get 2 * 2 * 3 * 5.

If I break 36 into it's prime factors, I would get 2 * 2 * 3 * 3.

The two number have the factors, 2, 2, and 3 in common.

The greatest common factor is then: 2 * 2 * 3, or 12.

The expression can be factored as: 12 ( 5 - 3)

6 0

4 years ago

3. A balancing balloon toy is in the shape of a hemisphere (half-sphere) attached to the base of a cone. If the toy is 4ft tall

Katen [24]

Answer:

The volume of the toy is $V=5.23\ ft^3$

Step-by-step explanation:

step 1

Find the volume of the hemisphere

The volume of the hemisphere is given by the formula

$V=\frac{2}{3}\pi r^{3}$

In this problem, the wide of the toy is equal to the diameter of the hemisphere

$D=2\ ft$

$r=2/2=1\ ft$ ----> the radius is half the diameter

substitute

$V=\frac{2}{3} \pi (1)^{3}=\frac{2}{3} \pi\ ft^3$

step 2

Find the volume of the cone

The volume of the cone is given by

$V=\frac{1}{3}\pi r^{2}h$

we know that

The radius of the cone is the same that the radius of the hemisphere

$r=1\ ft$

The height of the cone is equal to subtract the radius of the hemisphere from the height of the toy

$h=4-1=3\ ft$

substitute the given values

$V=\frac{1}{3}\pi (1)^{2}(3)=\pi\ ft^3$

step 3

Find the volume of the toy

we know that

The volume of the toy, is equal to the volume of the cone plus the volume of the hemisphere.

$V=(\frac{2}{3} \pi+\pi)\ ft^3$

$V=(\frac{5}{3}\pi)\ ft^3$

assume

$\pi=3.14$

$V=\frac{5}{3}(3.14)=5.23\ ft^3$

5 0

4 years ago

-1 and 3/5 divided by (-2/3) as a mixed number

goblinko [34]

Answer:

2 2/5

Step-by-step explanation:

change -1 3/5 to an improper fraction

-1 3/5 = -(5*1+3)/5 = -8/5

-1 3/5 ÷ -2/3 =

-8/5 ÷-2/3

copy dot flip

-8/5 * -3/2

24/10

divide top and bottom by 2

12/5

change back to a mixed number

5 goes into 12 2 times (5*2=10) with 2 left over

2 2/5

4 0

3 years ago

I need help pls help

Andreyy89

Answer:

[?] = 4

(the complete term is $4\frac{1}{2}\ \text{cups}$ )

Step-by-step explanation:

$8\ \text{cups} - 1\frac{1}{3}\ \text{cups} - 2\frac{1}{6}\ \text{cups} = (8-1-2)\ \text{cups} + \frac{-\frac{6}{3} - 1}{6}\ \text{cups} = 5\ \text{cups} + \frac{-3}{6}\ \text{cups} = 5\ \text{cups} + \frac{-1}{2}\ \text{cups} = 4\ \text{cups} + \frac{2 - 1}{2}\ \text{cups}$

7 0

2 years ago